We verify the validity of our approach by explicitly demonstrating Li and Haldane's bulk-boundary conjecture [1]}, for the first time in a gauge theory, both analytically in perturbation theory for an infinite systems, as well as numerically on a torus at arbitrary coupling [2]}. We also reconstruct the Entanglement Hamiltonian, using an ansatz based on the Bisognano-Wichmann theorem [3]}, [4]}, and find good agreement with expectations from the theorem [5]} in the topological ordered and trivial phase, as well as at the critical point \(\epsilon =\epsilon _c\) .
Using the closure of the `Entanglement Gap' [1]} of the ES as an indicator, we can determine the critical coupling \(\epsilon _c\)  to within 10% accuracy [7]}, even on very small lattices \(N_x \times N_y = 6\times 4\)  [2]}.
